Question

A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution.

X	0	1	2	3	4
P(X)	0.1	0.1		0.1	0.6

Determine P(x=2):    

Determine P(x≥3):   

Determine P(x<3):   

Determine the mean number of customers:  

Determine the standard deviation of the number of customers

Answer 1

Solution :

The sum of the probability is equal to 1 .

P(X) = 1

(a)

P(x = 2) = 1 - 0.1 - 0.1 - 0.1 - 0.6 = 0.1

(b)

P(x 3) = P(x = 3) + P(x = 4) = 0.1 + 0.6 = 0.7

(c)

P(x < 3) = P(x = 0) + P(x = 1) + P(x = 2) = 0.1 + 0.1 + 0.1 = 0.3

(d)

x	P(x)	x * P(x)	x2 * P(x)
0	0.1	0	0
1	0.1	0.1	0.1
2	0.1	0.2	0.4
3	0.1	0.3	0.9
4	0.6	2.4	9.6
Sum	1	3	11

Mean = = X * P(X) = 3

(e)

Standard deviation =

=X ² * P(X) - ²

=  11 - 3²

= 1.4142